There is disclosed in the patent application, now U.S. Pat. No. 3,580,471, issued May 25, 1971, in copending U.S. application Ser. No. 143,391, filed May 14, 1971, now abandoned and in copending U.S. application Ser. No. 433,978, filed Jan. 16, 1974, a collapsible cellular box partition and the method and apparatus for the continuous manufacture of such partition respectively. Copending U.S. application Ser. No. 293,941, filed Oct. 2, 1972, now U.S. Pat. No. 3,813,999, issued June 4, 1974, discloses and claims the apparatus for combining such collapsible cellular partitions with a box blank to form a collapsed shipping container which can be set up into a partition box while the present application discloses and claims the method carried out by the apparatus of the copending application Ser. No. 293,941 and the new uses of such apparatus for combining other forms of partitions with a box blank and making a double wall thickness box.